Optimal foraging strategies for territorial competitors

Many animals such as albatrosses are known to exhibit foraging patterns where the distances they travel in a given direction are drawn from a heavy tailed Levy distribution. Previous studies have shown under sparse resources, solitary foragers perform an optimally efficient search with Levy exponent equal to 2. However, in nature, there also exist situations where multiple foragers interact with each other either cooperatively or competitively. We develop a stochastic agent-based simulation that models foraging with competitive interactions. In our simulations each forager has a territory with a certain size around itself which is not accessible by the others. We show that by increasing the size of the territory, and number of agents, the efficiency of the search decreases, and the optimal Levy exponent shifts toward values larger than 2, indicating that more localized searches are more efficient in the presence of competition. Finally, we show that the variance among the efficiencies of the agents increases with increasing Levy exponent. Thus, by performing more localized searches, foragers might increase mean efficiency, but with the risk of increasing fluctuations in efficiency.